[blackbear_]

Not sure I am following; typical neural network training via stochastic gradient descent does not require Jacobian inversion.

Less popular techniques like normalizing flows do need that but instead of SVD they directly design transformations that are easier to invert.

[imtringued]

The idea is that you already have a trained model of the dynamics of a physical process and want to include it inside your quadratic programming based optimizer. The standard method is to linearize the problem by materializing the Jacobian. Then the Jacobian is inserted into the QP.

QPs are solved by finding the roots (aka zeroes) of the KKT conditions, basically finding points where the derivative is zero. This is done by solving a linear system of equations Ax=b. Warm starting QP solvers try to factorize the matrices in the QP formulation through LU decomposition or any other method. This works well if you have a linear model, but it doesn't if the model changes, because your factorization becomes obsolete.